We can also spend more time to train the \(d=64\)  decoder, and then compare the performance of the neural decoders to the minimum-weight perfect matching algorithm (MWPM) in fig:comparisontoMWPM.
The “star” points are the logical accuracies of MWPM, where each one is evaluated by 3000 trials.
The \(d=16\)  decoder corresponding to the solid line and the \(d=64\)  decoder corresponding to the dashed line are from the strict training policy.
The \(d=64\)  decoder corresponding to the solid line is obtained by doing more training while having the same network architecture.
We see that without the strict training policy, the performance of the neural decoder is almost identical to MWPM for a decent range of physical error rates.
We can also compare to the renormalization group (RG) decoder in [1]}, where the authors have shown a threshold of \(8.2\%\)  when using \(2\times 1\)  unit cell, and claim a threshold around \(9.0\%\)  if using \(2\times 2\)  unit cell.
With the strict training policy, our neural decoder is slightly better or at least comparable to the RG decoder, while without the policy our neural decoder is clearly better for \(d\le 64\) .
